CN107092580A - A kind of curve-fitting method minimum based on relative error - Google Patents
A kind of curve-fitting method minimum based on relative error Download PDFInfo
- Publication number
- CN107092580A CN107092580A CN201710203823.8A CN201710203823A CN107092580A CN 107092580 A CN107092580 A CN 107092580A CN 201710203823 A CN201710203823 A CN 201710203823A CN 107092580 A CN107092580 A CN 107092580A
- Authority
- CN
- China
- Prior art keywords
- value
- mrow
- coefficient
- curve
- msub
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/15—Correlation function computation including computation of convolution operations
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Computational Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Data Mining & Analysis (AREA)
- Algebra (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Computing Systems (AREA)
- Complex Calculations (AREA)
Abstract
The present invention relates to a kind of curve-fitting method minimum based on relative error, this method constructs the functional form of matched curve on the basis of the basic function collection of linear independence, each term coefficient in the function of matched curve is provided using the method for iterative calculation, coefficient is substituted into the theoretical value obtained after fitting function has the characteristics of relative error quadratic sum is minimum, curve-fitting method of the present invention has the characteristics of relative error quadratic sum is minimum, avoid the loss of learning problem of least square method presence, and the curve-fitting method that the present invention is provided, logicality is strong, it is easily programmed, and method is simple.
Description
Technical field
The present invention relates to a kind of curve-fitting method minimum based on relative error, belong to numerical analysis and reliability engineering
Field.
Background technology
There are many functions in scientific experimentation and engineer applied, its analytical expression is ignorant.Such as, inertia device
Part can be varied from the extension of period of storage, its performance and parameter, but the change procedure is only capable of the side by experimental observation
Method measures a series of node xiOn value fi.Now the problem is that seeking to test the approximating function y (x) of point sequence, or use geometry language
It is exactly to seek a curve y (x) to be fitted (smooth) this n point for speech.
Traditional curve-fitting method is to use least square method, it is desirable to
Wherein,
Then y (x) is called f (x) on weight coefficient { ωiLeast square approximation, and deserve to be called and state criterion and seek approximating function y
(x) method is least square method.In above formula, { ωj(x) it is } collection of functions of linear independence, { ajIt is corresponding coefficient set.
From formula (1) from the point of view of the expression formula of least square method, the absolute error quadratic sum minimum in each point is taken as coefficient
{a* jSelection principle.But this, which has a problem that, is, in difference xiAnd xj, there are y (x at placei)<<y(xj), if measurement error by
Fixed factor Δ r causes, i.e.,
fi=(1+ Δ r) y (xi)
fj=(1+ Δ r) y (xj)
Now, there is fi-y(xi)=Δ r y (xi)<<Δr y(xj)=fj-y(xj), therefore, have
(fi-y(xi))2<<(fj-y(xj))2
I.e.
(fi-y(xi))2+(fj-y(xj))2≈(fj-y(xj))2
It means that in xiThe information at place is lost.
Accordingly, it would be desirable to for above-mentioned situation, propose a kind of optimal curve-fitting method.
The content of the invention
It is an object of the invention to the drawbacks described above for overcoming prior art, there is provided a kind of curve minimum based on relative error
Approximating method, this method by way of accurate Iterative, can provide each term coefficient of fitting function, make the relative of fitting
Error sum of squares is minimum, it is to avoid the loss of learning problem that least square method is present.
What the above-mentioned purpose of the present invention was mainly achieved by following technical solution：
A kind of curve-fitting method minimum based on relative error, including：
Given measurement sequence { fiAnd weight coefficient sequence { ωi, i=1,2 ..., n；
Determine the basic function collection of linear independence
Construction measurement sequence { fiIunction for curve ψ (x), orderWherein { ajFor it is corresponding not
Know coefficient set；
Coefficient set { a is determined according to optiaml ciriterionjOptimal value { a*j, i.e., optimal value is solved according to equation below
{a*j}：
Wherein：y(xi) it is the corresponding ψ (x of i-th of discrete pointi) on weight coefficient sequence { ωiMinimum relative error
Approach；
By the optimal value { a*jIunction for curve ψ (x) is substituted into, obtain the function expression y of optimal fitting curve
(x)：
In above-mentioned curve-fitting method, the coefficient set { a is determined according to optiaml ciriterionjOptimal value { a*j, enter one
Step is equivalent to solve optimal value { a* according to equation belowj}：
In above-mentioned curve-fitting method, optimal value { a* is solvedjSpecific method it is as follows：
(1) coefficient a, is solved according to equation below0,a1,…,amInitial value；
(2), coefficient a0,a1,…,amInitial value substitute into equation below solve gi：
(3), by giSubstitute into and equation below (6) is obtained in formula (3), and coefficient a is obtained according to equation below (6) solution0,
a1,…,amOne group be newly worth：
(4), return to step (2), by the coefficient a0,a1,…,amOne group of new value as initial value substitute into formula (5), follow
Ring is calculated, until calculating obtained coefficient a0,a1,…,amThe new value of L groups calculate obtained coefficient a with last0,a1,…,
amL-1 groups newly value between deviation meet require, then take the L groups newly value as optimal value { a*j}；Wherein：L is just
Integer.
In above-mentioned curve-fitting method, coefficient a in the step (4)0,a1,…,amL groups newly value and last meter
Obtained coefficient a0,a1,…,amThe new value of L-1 groups between deviation meet requirement and refer to：Coefficient a0,a1,…,amL
The new value of group and coefficient a0,a1,…,amL-1 groups before newly corresponding each coefficient is after decimal point in value p value it is equal
It is identical, i.e., a in the new value of L groups0With a in L-1 groups newly value0The value of p is identical before after decimal point, and L groups are newly in value
a1With a in L-1 groups newly value1The value of p is identical before after decimal point ... ..., a in the new value of L groupsmNewly it is worth with L-1 groups
In amThe value of p is identical before after decimal point, wherein：P is positive integer.
In above-mentioned curve-fitting method, coefficient a in the step (1)0,a1,…,amInitial value asked by equation below
Solution is obtained：
In above-mentioned curve-fitting method, coefficient a in the step (3)0,a1,…,amOne group of new value pass through it is following public
Formula is solved and obtained：
The present invention having the beneficial effect that compared with prior art：
(1), The present invention gives a kind of curve-fitting method minimum based on relative error, in the basic function of linear independence
The functional form of matched curve is constructed on the basis of collection, each term system in the function of matched curve is provided using the method for iterative calculation
Number, coefficient is substituted into the theoretical value obtained after fitting function has the characteristics of relative error quadratic sum is minimum.
(2), The present invention gives a kind of curve-fitting method minimum based on relative error, this method is that one kind is different from
The new method of the appraisal curve fitting of least square method, with relative error quadratic sum it is minimum the characteristics of, it is to avoid least square
The loss of learning problem that method is present.
(3), the present invention solves the coefficient of fitting function using iterative calculation, solves what Nonlinear System of Equations can not be solved
Problem, and the present invention is by way of accurate Iterative, so as to get and the relative error quadratic sum of fitting is minimum.
(4), the curve-fitting method that the present invention is provided, logicality is strong, it is easy to program, and method is simple, it is easy to accomplish.
Brief description of the drawings
Fig. 1 is the present invention based on the minimum curve fitting routine figure of relative error；
Fig. 2 is measurement sequence given in the embodiment of the present invention；
Fig. 3 is the iterative process of the embodiment of the present invention；
Fig. 4 is the matched curve that the embodiment of the present invention is obtained；
Fig. 5 is that the matched curve that the embodiment of the present invention is obtained is compared figure with least square method.
Embodiment
The present invention is described in further detail with specific embodiment below in conjunction with the accompanying drawings：
The invention provides a kind of curve-fitting method minimum based on relative error, in the basic function collection of linear independence
On the basis of construct matched curve functional form, each term coefficient in the function of matched curve is provided using the method for iterative calculation,
Coefficient is substituted into the theoretical value obtained after fitting function has the characteristics of relative error quadratic sum is minimum.
It is as shown in Figure 1 the flow chart of the invention based on the minimum curve-fitting method of relative error, the present invention is based on phase
The curve-fitting method minimum to error comprises the following steps that the relative error quadratic sum of measurement sequence and fitting sequence is minimum：
First, measurement sequence { f is giveniAnd weight coefficient sequence { ωi, i=1,2 ..., n.
2nd, the basic function collection of linear independence is determined
3rd, construction measurement sequence { fiIunction for curveWherein { ajIt is corresponding unknown system
Manifold.
4th, the coefficient set { a is determined according to optiaml ciriterionjOptimal value { a*j}.To make relative error quadratic sum minimum,
Have
Wherein：y(xi) it is the corresponding ψ (x of i-th of discrete pointi) on weight coefficient sequence { ωiMinimum relative error
Approach.
Define m+1 meta-function H (a0,a1,…,am) be
From the necessary condition of function of many variables extreme value, minimum point should be met
Above formula is equivalent to
But due in above formula, each term coefficient a0,a1,…,amOccur in the denominator, it is difficult to solve.Intend asking using iteration
Solution.Optimal value { a* can be solved by the following methodj, specifically include following steps：
(1) coefficient a, is solved according to equation below0,a1,…,amInitial value；
Define m+1 meta-functions H1(a0,a1,…,am) be
From the necessary condition of function of many variables extreme value, minimum point should be met
Above formula is equivalent to
Can must be to coefficient a0,a1,…,amA kind of computational methods of initial value are：
(2), coefficient a0,a1,…,amInitial value substitute into equation below and solve intermediate variable gi：
Then by giSubstitute into above-mentioned formula (3)：
It is equivalent to equation below：
I.e.：
(3), solved according to formula (6) and obtain coefficient a0,a1,…,amOne group be newly worth, solve coefficient a0,a1,…,am's
A kind of one group of computational methods being newly worth is：
(4), return to step (2), by coefficient a0,a1,…,amOne group of new value as initial value substitute into formula (5), again
Calculate gi, by giSubstitute into formula (3) and obtain formula (6), solved according to formula (6) and obtain coefficient a0,a1,…,amSecond group
New value, returns again to step (2), and this second group new value is substituted into formula (5) as initial value, the like, cycle calculations, until meter
Obtained coefficient a0,a1,…,amThe new value of L groups calculate obtained coefficient a with last0,a1,…,amL-1 groups it is new
Deviation between value, which is met, to be required, i.e., every error coefficient tends to a fixed value, then takes the new value of the L groups as optimal value
{a*j}；Wherein：L is positive integer.
Coefficient a in above-mentioned steps (4)0,a1,…,amThe new value of L groups calculate obtained coefficient a with last0,a1,…,
amThe new value of L-1 groups between deviation meet requirement and refer to：Coefficient a0,a1,…,amL groups newly value with coefficient a0,a1,…,
amL-1 groups value all same of p before newly corresponding each coefficient is after decimal point in value, i.e., L groups are new be worth in a0
With a in L-1 groups newly value0The value of p is identical before after decimal point, a in the new value of L groups1With a in L-1 groups newly value1
The value of p is identical before after decimal point ... ..., a in the new value of L groupsmWith a in L-1 groups newly valuemP before after decimal point
Value it is identical, wherein：P is positive integer, such as p takes preceding 10 corresponding phase after 10, i.e., m+1 coefficient decimal point in the present embodiment
Together, then it is assumed that meet deviation requirement.
5th, by optimal value { a*jIunction for curve ψ (x) is substituted into, obtain the function expression y of optimal fitting curve
(x)：
The data of test can be carried out curve fitting in actual applications using the inventive method, for being carried out to equipment
Life appraisal, judges the term of validity and storage life with pre- measurement equipment.
Embodiment 1
If given independent variable is { xiCorresponding measurement sequence { fi, i=1,2 ..., n；Wherein n=10, is illustrated in figure 2
The measurement sequence given in the embodiment of the present invention, data occurrence is shown in Table 1.It is fitted using linearity curve, chooses two bases
FunctionWithThus the fitting function constructed is y (x)=a1x-a2。
Table 1
| i | xi | fi |
| 1 | 1.098612288668110 | -4.600149226776579 |
| 2 | 1.609437912434100 | -3.491366950083786 |
| 3 | 2.079441541679836 | -3.198534261445385 |
| 4 | 2.397895272798371 | -2.970195249042164 |
| 5 | 2.708050201102210 | -2.361160845794877 |
| 6 | 2.890371757896165 | -1.891649046236146 |
| 7 | 2.995732273553991 | -1.557220146752500 |
| 8 | 3.091042453358316 | -1.200295929708821 |
| 9 | 3.178053830347946 | -0.8782354957945757 |
| 10 | 3.218875824868201 | -0.7380696519250566 |
Using the method for solving of the present invention, coefficient initial value is a1=2.037561490172089, a2=
7.419031362900331, then finally try to achieve a after 8 times iterate to calculate1=2.200474914250277, a2=
7.987855655876523, i.e., iterate to calculate obtained a with the 7th time1、a2Preceding 10 correspondent equals, are optimal value after decimal point.
Iterative process is as shown in figure 3, wherein Fig. 3 a and Fig. 3 b represent a respectively1、a2Iterative process.A1And a2Substituting into fitting function is
Y (x)=a1x-a2In in the ideal data tried to achieve such as Fig. 4 shown in " * " point, it is bent that Fig. 4 show the fitting that the embodiment of the present invention obtains
In line, figure "." it is expressed as measured value.
Data to table 1 can also use least square method, and the coefficient of solution is a1=1.696152760852661, a2=
6.574443934342034.It is illustrated in figure 5 the matched curve that the embodiment of the present invention obtains and is compared figure, Fig. 5 with least square method
In " dotted line " be the obtained matched curve of least square method, " solid line " is the matched curve that the inventive method is obtained, " chain-dotted line "
For measurement sequence { fiMatched curve.In order to compare the difference of two methods, ask for respectively
(1) least square method：0.2920199887220504；
(2) the inventive method：0.2037926358513409.
As can be seen that the relative error quadratic sum that the present invention is provided is minimum, and without loss of learning problem.
It is described above, it is only an embodiment of the invention, but protection scope of the present invention is not limited thereto, and is appointed
What those familiar with the art the invention discloses technical scope in, the change or replacement that can be readily occurred in, all
It should be included within the scope of the present invention.
Unspecified part of the present invention belongs to general knowledge as well known to those skilled in the art.
Claims (6)
1. a kind of curve-fitting method minimum based on relative error, it is characterised in that：Including：
Given measurement sequence { fiAnd weight coefficient sequence { ωi, i=1,2 ..., n；
Determine the basic function collection of linear independenceJ=1,2 ..., m；
Construction measurement sequence { fiIunction for curve ψ (x), orderWherein { ajIt is corresponding unknown system
Manifold；
Coefficient set { a is determined according to optiaml ciriterionjOptimal value { a*j, i.e., optimal value { a* is solved according to equation belowj}：
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&omega;</mi>
<mi>i</mi>
</msub>
<mfrac>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>f</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>y</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
<mrow>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&omega;</mi>
<mi>i</mi>
</msub>
<mfrac>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>f</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>&psi;</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
<mrow>
<msup>
<mi>&psi;</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein：y(xi) it is the corresponding ψ (x of i-th of discrete pointi) on weight coefficient sequence { ωiMinimum relative error approach；
By the optimal value { a*jIunction for curve ψ (x) is substituted into, obtain the function expression y (x) of optimal fitting curve：
2. curve-fitting method according to claim 1, it is characterised in that：The coefficient set is determined according to optiaml ciriterion
{ajOptimal value { a*j, further it is equivalent to solve optimal value { a* according to equation belowj}：
3. curve-fitting method according to claim 1 or 2, it is characterised in that：Solve optimal value { a*jSpecific method
It is as follows：
(1) coefficient a, is solved according to equation below0,a1,…,amInitial value；
(2), coefficient a0,a1,…,amInitial value substitute into equation below solve gi：
(3), by giSubstitute into and equation below (6) is obtained in formula (3), and coefficient a is obtained according to equation below (6) solution0,
a1,…,amOne group be newly worth：
(4), return to step (2), by the coefficient a0,a1,…,amOne group of new value be used as initial value to substitute into formula (5), circulation meter
Calculate, until calculating obtained coefficient a0,a1,…,amThe new value of L groups calculate obtained coefficient a with last0,a1,…,am's
Deviation between L-1 groups are newly worth meets requirement, then takes the new value of the L groups as optimal value { a*j}；Wherein：L is just whole
Number.
4. curve-fitting method according to claim 3, it is characterised in that：Coefficient a in the step (4)0,a1,…,am
The new value of L groups calculate obtained coefficient a with last0,a1,…,amThe new value of L-1 groups between deviation meet requirement and be
Refer to：Coefficient a0,a1,…,amL groups newly value with coefficient a0,a1,…,amNew corresponding each coefficient in value of L-1 groups
A during the value all same of p, i.e. L groups are newly worth before after decimal point0With a in L-1 groups newly value0P before after decimal point
Value it is identical, L groups newly value in a1With a in L-1 groups newly value1The value of p is identical before after decimal point ... ..., L groups
A in new valuemWith a in L-1 groups newly valuemThe value of p is identical before after decimal point, wherein：P is positive integer.
5. curve-fitting method according to claim 3, it is characterised in that：Coefficient a in the step (1)0,a1,…,am
Initial value by equation below solve obtain：
6. curve-fitting method according to claim 3, it is characterised in that：Coefficient a in the step (3)0,a1,…,am
One group of new value by equation below solve obtain：
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710203823.8A CN107092580A (en) | 2017-03-30 | 2017-03-30 | A kind of curve-fitting method minimum based on relative error |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710203823.8A CN107092580A (en) | 2017-03-30 | 2017-03-30 | A kind of curve-fitting method minimum based on relative error |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN107092580A true CN107092580A (en) | 2017-08-25 |
Family
ID=59646317
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710203823.8A Pending CN107092580A (en) | 2017-03-30 | 2017-03-30 | A kind of curve-fitting method minimum based on relative error |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107092580A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107505843A (en) * | 2017-09-15 | 2017-12-22 | 中国科学院长春光学精密机械与物理研究所 | A kind of Active thermal control optimization method of space optics payload |
| CN110197044A (en) * | 2019-06-11 | 2019-09-03 | 贵州大学 | Pattern automatic generation method based on fractals |
| CN110988825A (en) * | 2019-12-16 | 2020-04-10 | 西安电子工程研究所 | Radar seeker angle measurement curve fitting method |
-
2017
- 2017-03-30 CN CN201710203823.8A patent/CN107092580A/en active Pending
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107505843A (en) * | 2017-09-15 | 2017-12-22 | 中国科学院长春光学精密机械与物理研究所 | A kind of Active thermal control optimization method of space optics payload |
| CN107505843B (en) * | 2017-09-15 | 2020-05-15 | 中国科学院长春光学精密机械与物理研究所 | Active thermal control optimization method for space optical payload |
| CN110197044A (en) * | 2019-06-11 | 2019-09-03 | 贵州大学 | Pattern automatic generation method based on fractals |
| CN110197044B (en) * | 2019-06-11 | 2022-07-01 | 贵州大学 | Pattern automatic generation method based on fractal geometry |
| CN110988825A (en) * | 2019-12-16 | 2020-04-10 | 西安电子工程研究所 | Radar seeker angle measurement curve fitting method |
| CN110988825B (en) * | 2019-12-16 | 2022-11-22 | 西安电子工程研究所 | Radar seeker angle measurement curve fitting method |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107092580A (en) | A kind of curve-fitting method minimum based on relative error | |
| CN106324521B (en) | A kind of method of Combined estimator electrokinetic cell system parameter and state-of-charge | |
| CN104166731B (en) | A kind of overlapping community discovery system and method for social networks | |
| CN104133404B (en) | A kind of signal processing method and device | |
| CN109800449B (en) | Neural network-based aeroengine compression component characteristic correction method | |
| CN107273336A (en) | A kind of curve-fitting method based on least square method | |
| CN106154168B (en) | The method for estimating charge state of power cell of data-driven | |
| CN105043433B (en) | A kind of photoelectric encoder fast-compensation method based on neutral net | |
| CN106063132A (en) | On-chip analog-to-digital converter (adc) linearity test for embedded devices | |
| CN112434380A (en) | Aircraft wing weight estimation method | |
| CN115840184A (en) | Voltage transformer operation error analysis method, medium and terminal | |
| CN109408929A (en) | Determine the optimum design method of high voltage direct current resistance standard voltage divider grading ring | |
| CN110110406B (en) | Slope stability prediction method for achieving LS-SVM model based on Excel computing platform | |
| CN103093079B (en) | The uncertain tidal current analysis method of radial pattern power distribution network based on affine arithmetic | |
| CN113189513B (en) | Ripple-based redundant power supply current sharing state identification method | |
| CN105353359B (en) | Asynchronous radar network systematic error correction method | |
| CN107248864A (en) | The high-precision adc and conversion method calibrated based on weight | |
| CN114583767A (en) | Data-driven wind power plant frequency modulation response characteristic modeling method and system | |
| CN107526294B (en) | Intelligent identification method for thermal field temperature-silicon single crystal diameter nonlinear time lag system | |
| CN103925939B (en) | The calibration compensation method of a kind of photoelectric coding device gamut | |
| CN110186482B (en) | Method for improving drop point precision of inertial guidance spacecraft | |
| CN107425523A (en) | A kind of complicated electric power system kinematic error identification and auto-correction method and system | |
| CN103400201A (en) | Method for solving state estimation problem taking maximum normal rate of measurement point as target | |
| CN113283784B (en) | Reliability inverse problem model based on interval optimization algorithm and solving method thereof | |
| CN115455347A (en) | MEMS accelerometer hybrid error modeling compensation method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20170825 |